Partial deconfinement in color superconductivity

We analyze the fate of the unbroken $\mathrm{SU}(2)$ color gauge interactions for two-light-flavor color superconductivity at nonzero temperature. Using a simple glueball Lagrangian model, we compute the deconfining or confining critical temperature and show that it is smaller than the critical temperature for the onset of the superconductive state itself. The breaking of Lorentz invariance, induced already at zero temperature by the quark chemical potential, is shown to heavily affect the value of the critical temperature and all of the relevant features related to the deconfining transition. Modifying the Polyakov loop model to describe the $\mathrm{SU}(2)$ immersed in the diquark medium, we argue that the deconfinement transition is second order. Having constructed part of the equation of state for the two-color superconducting phase at low temperatures, our results may be relevant for the physics of compact objects featuring a two-flavor color superconductive state.